How can information theory inform interdisciplinary curriculum and software development?
Information theory
Information theory is a branch of applied mathematics and computer science that deals with the quantification, storage, transmission, and manipulation of information. We take an abstract approach to our study of information.
Information theory seeks to measure the amount of information contained in a message or signal and how efficiently it can be transmitted or stored.
In this way, our projects define information using a curricular perspective.
Quantitative history
Historie Quantitative by Pierre Chaunu
Mathematical sociology
Journal of Mathematical Sociology
Curriculum and software development
Design, development, implementation, and evaluation of computational curricular materials
Research projects
ECHO: Education, Community, and Health Observations
Information and spatial segregation
Teaching statistical learning and mathematical modeling
Theory and quantification
Project group 1: Spatial information and racial isolation
How do patterns of racial segregation inform education, community, and health outcomes?
Historical legacies of injustice
Traditional modeling approaches
Modern computational tools
Dividing walls
Geometric approach
We adopt a topological model for spatial segregation on a geographical area, \(G\) to develop a theory of dividing walls.
Builds on the topological and topographical work of Short (2011).
Theorem 1. Given any configuration of blue and green towns, there is a dividing wall that separates blue towns from green towns.
Geographic area with neighborhood units
Theorem 1. Given any configuration of blue and green towns, there is a dividing wall that separates blue towns from green towns.
Geographic area with neighborhood units
Theorem 1. Given any configuration of blue and green towns, there is a dividing wall that separates blue towns from green towns.
Geographic area with wall dividing neighborhood units
Is there a dividing wall for an island with coastal towns?
Island with coastal towns
Is there a dividing wall for an island with coastal towns?
Minimal configuration
Alternating configuration (left) and non-alternating configuration (right).
Theorem 2. Alternating configurations of towns do not have a dividing wall, whereas non-alternating configurations of towns do have a dividing wall.
Algebraic approach
We then develop a algebraic modeling approach using methods from mathematical sociology.
Segregation indices
Dissimilarity index: Measures the proportion of one group’s population that would need to move to achieve an even distribution across all areas. It ranges from 0 to 1, with higher values indicating greater segregation.
Isolation index: Measures the extent to which members of a particular group are surrounded by others from the same group. It represents the percentage of people from a specific group who would need to change neighborhoods to achieve an even distribution. Higher values indicate higher isolation and segregation.
Algebraic approach
We then develop a algebraic modeling approach using methods from mathematical sociology.
Segregation indices
Exposure index: Measures the extent to which members of one group are exposed to members of another group. It quantifies the likelihood that a randomly selected individual from one group will encounter individuals from another group. Higher values indicate higher exposure and lower segregation.
Concentration index: Measures the extent to which a particular group is concentrated in specific areas or neighborhoods. It reflects the degree of clustering or dispersion of the group’s population across geographic units.
Gini index: Measure of income inequality, but it can also be adapted to measure residential segregation. It provides a summary measure of the overall distribution of different groups across neighborhoods.
\(n\) is the number of neighborhoods in a geographic region,
\(b_i\) is the number of Black household units in neighborhood \(i\),
\(B\) is the total number of Black household units in the geographic region,
\(w_i\) is the number of non-Black household units in neighborhood \(i\),
\(W\) is the total number of non-Black household units in the geographic region,
Co-authored student research poster.
Computational approach
Teaching computational methods and open source tools makes for efficient and accurate learning. In about 20 lines of code, there is an immediate intersection.
black_georgetown_sc_2020 <-get_acs(geography ="tract", state ="SC",county ="Georgetown",variable ="B02001_003", # Black or African American Alonegeometry =TRUE)
Getting data from the 2018-2022 5-year ACS
Downloading feature geometry from the Census website. To cache shapefiles for use in future sessions, set `options(tigris_use_cache = TRUE)`.
